In [[1]}], Jun Li introduces the notion of stacks of expanded degenerations and pairs for variety cases, whose appearance is stimulated by Gieseker's degeneration of some moduli space and Floer-Donaldson theory as pointed out in [[2]}]. These stacks are crucial to constructing good degenerations of moduli spaces of stable morphisms, ideal sheaves and stable pairs [[1]}, [4]}, [5]}], and are furtherly investigated through several comparable approaches and generalized to the twisted version in [[6]}]. In this subsection, we will recall the construction of stacks of expanded degenerations and pairs in [[7]}] for the case of Deligne-Mumford stacks, which is a direct generalization of Li's approach [[1]}, [2]}].
